2011/01/31 by Anne Moreau, A. Moreau, Oksana Yakimova +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic group #Algebraic number #Algebraic structures and combinatorial models #Field (mathematics) #Lie algebra #Nonlinear Waves and Solitons #Quotient #Reductive group #Simple (philosophy) #Type (biology) #Zero (linguistics) #math.RT
paper · pdf · doi:10.1093/imrn/rnr184
published as International Mathematics Research Notices (2011) 45 pages · 35 pages, 5 figures; International Mathematics Research Notices (2011) 45 pages
openalex publication_date 2011/10/12 · arxiv created 2011/11/22 · arxiv updated 2011/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A connected algebraic group Q defined over a field of characteristic zero is quasi-reductive if there is an element of of reductive type, that is such that the quotient of its stabilizer by the center of Q is a reductive subgroup of . Such groups appear in harmonic analysis when unitary representations are studied. In particular, over the field of real numbers they turn out to be the groups with discrete series and their irreducible unitary square integrable representations are parameterised by coadjoint orbits of reductive type. Due to the results of Duflo, coadjoint representation of a quasi-reductive Q possesses a so-called maximal reductive stabiliser and knowing this subgroup, defined up to a conjugation in Q, one can describe all coadjoint orbits of reductive type. In this paper, we consider quasi-reductive parabolic subalgebras of simple complex Lie algebras as well as seaweed subalgebras of and describe the classes of their maximal reductive stabilizers.